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<p>The selection of the most suitable substitution box (S-box) is a key factor in enhancing the security and efficiency of modern cryptographic systems. As multiple S-boxes are available, identifying the one that provides the highest level of resistance against potential attacks is a complex decision-making task. To address this challenge, this study introduces a novel decision-making model called the linguistic <i>pq</i>-rung orthopair neural network (L<i>pq</i>-RONN), which utilizes linguistic <i>pq</i>-rung orthopair fuzzy information to handle uncertainty more effectively. This fuzzy framework offers a flexible and accurate way to represent linguistic assessments during the evaluation process. Initially, the linguistic <i>pq</i>-rung orthopair fuzzy set and a series of linguistic aggregation operators, such as the linguistic weighted and linguistic geometric weighted operators, are defined and their fundamental properties are discussed. The proposed L<i>pq</i>-RONN model integrates these operators within a neural network architecture to enhance decision-making performance. The model is then applied to a real-world problem of selecting the most suitable S-box for image encryption, based on expert opinions and multiple evaluation criteria. The results show that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{\mathfrak{R}}_{1}\)</EquationSource> </InlineEquation> (AES S-box) is the most effective alternative, providing superior encryption strength and stability. Additionally, the entropy method and linguistic distance measure are employed to compute attribute weights objectively. We also perform a sensitivity analysis to examine how the model responds to changes in input parameters and to assess the robustness of the decision-making process. Finally, comparative analysis with other existing MCDM techniques demonstrates that the proposed model is reliable, efficient, and provides improved decision support in cryptographic applications. The advantages and limitations of the proposed method are also discussed in the context of practical implementation.</p>

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Linguistic pq-rung orthopair neural network approach for optimal S-Box selection in image encryption

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Nawab Ali,
  • Saleem Abdullah,
  • Shakoor Muhammad,
  • Hameed Gul Ahmadzai

摘要

The selection of the most suitable substitution box (S-box) is a key factor in enhancing the security and efficiency of modern cryptographic systems. As multiple S-boxes are available, identifying the one that provides the highest level of resistance against potential attacks is a complex decision-making task. To address this challenge, this study introduces a novel decision-making model called the linguistic pq-rung orthopair neural network (Lpq-RONN), which utilizes linguistic pq-rung orthopair fuzzy information to handle uncertainty more effectively. This fuzzy framework offers a flexible and accurate way to represent linguistic assessments during the evaluation process. Initially, the linguistic pq-rung orthopair fuzzy set and a series of linguistic aggregation operators, such as the linguistic weighted and linguistic geometric weighted operators, are defined and their fundamental properties are discussed. The proposed Lpq-RONN model integrates these operators within a neural network architecture to enhance decision-making performance. The model is then applied to a real-world problem of selecting the most suitable S-box for image encryption, based on expert opinions and multiple evaluation criteria. The results show that \(\:{\mathfrak{R}}_{1}\) (AES S-box) is the most effective alternative, providing superior encryption strength and stability. Additionally, the entropy method and linguistic distance measure are employed to compute attribute weights objectively. We also perform a sensitivity analysis to examine how the model responds to changes in input parameters and to assess the robustness of the decision-making process. Finally, comparative analysis with other existing MCDM techniques demonstrates that the proposed model is reliable, efficient, and provides improved decision support in cryptographic applications. The advantages and limitations of the proposed method are also discussed in the context of practical implementation.